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A102365 Triangle T(n,k), 0 <= k <= n, read by rows: given by [ 1, 0, 3, 0, 5, 0, 7, 0, 9, 0, ...] DELTA [ 0, 1, 0, 2, 0, 3, 0, 4, 0, 5, 0, ...] where DELTA is the operator defined in A084938. 3
1, 1, 0, 1, 1, 0, 1, 5, 1, 0, 1, 18, 15, 1, 0, 1, 58, 129, 37, 1, 0, 1, 179, 877, 646, 83, 1, 0, 1, 543, 5280, 8030, 2685, 177, 1, 0, 1, 1636, 29658, 82610, 56285, 10002, 367, 1, 0, 1, 4916, 159742, 756218, 919615, 335162, 34777, 749, 1, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,8

COMMENTS

Generalized Eulerian numbers A008292.

Reversal of A211399. - Philippe Deléham, Feb 12 2013

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

FORMULA

T(n, k) = (n-k)*T(n-1, k-1) + (2*k+1)*T(n-1, k) with T(0, 0) = 1, T(0, k) = 0 if k > 0, T(n, k) = 0 if k < 0.

Sum_{k>=0} T(n, k)*2^k = A001147(n).

Sum_{k>=0} T(n, k) = A014307(n). - Philippe Deléham, Mar 19 2005

EXAMPLE

Triangle begins:

  1;

  1,  0;

  1,  1,   0;

  1,  5,   1,  0;

  1, 18,  15,  1, 0;

  1, 58, 129, 37, 1, 0; ...

MATHEMATICA

T[0, 0] := 1;  T[n_, -1] := 0;  T[n_, n_] := 0; T[n_, k_] := T[n, k] = (n - k)*T[n - 1, k - 1] + (2*k + 1)*T[n - 1, k]; Join[{1}, Table[If[k < 0, 0, If[k >= n, 0, T[n, k]]], {n, 1, 5}, {k, 0, n}] // Flatten] (* G. C. Greubel, Jun 30 2017 *)

CROSSREFS

Diagonals: A000007, A000012, A050488, A142965, A142966.

Columns: A000012, A000340, A156922, A156923, A156924.

Sequence in context: A211399 A265192 A157012 * A269945 A322013 A102259

Adjacent sequences:  A102362 A102363 A102364 * A102366 A102367 A102368

KEYWORD

nonn,easy,tabl

AUTHOR

Philippe Deléham, Feb 22 2005

STATUS

approved

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Last modified June 24 00:06 EDT 2021. Contains 345403 sequences. (Running on oeis4.)